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Hi all, Just wanted to find out what formula is being used by Mplus to calculate the bias in biascorrected bootstrap confidence intervals. Is it the formula that Efron had established or is the bias being calculated some other way? Thank you very much. Yours, Viktoriya Magid SUNY at Buffalo 

bmuthen posted on Tuesday, April 19, 2005  12:04 pm



Please see the KcKinnon et al 2004 reference in the Mplus Version 3 User's Guide. I believe that is the Efron version. 

bmuthen posted on Tuesday, April 19, 2005  12:07 pm



P.S. I meant to say MacKinnon. 


Dear Dr. Muthen, Thank you for getting back to me. From what I know, the Efron formula considers both bias and acceleration, however MacKinnon (2004) considered only the bias in his simulation (he found that considering the acceleration in addition to the bias did not improve the accuracy of confidence intervals). Hence, to elaborate on my earlier question, does Mplus consider both bias and acceleration in computing the biascorrected bootstrap confidence intervals (as has been suggested by Efron in his formula) or does it consider the bias only (as has been done by MacKinnon, 2004)? Thank you in advance, Yours, Viktoriya 


Mplus considers bias only as in MacKinnon. 


Thank you very much. 

Andrew posted on Wednesday, June 08, 2005  12:33 pm



Does Mplus have a way to change the seed of the random bootstrapping algorithm? All the seed options in ANALYSIS: don't seem to do anything, and the bootstrap results don't appear to vary across runs. The only thing that I can do to get variation across bootstrap results is to change the number of bootstraps. 


No, there is no option to change to seed in bootstrap. 


I am using a subset of a longitudinal data set (as not everyone attended a focus group). The ones who dropped out were mostly disadvantaged individuals with less education, from lower SES level etc. I want to run a SEM model (with 4 latent variables) and 3 observed variables (all binary). I use the WLSMV estimator. So my question is: 1) is it possible to run a SEM model with Heckman correction for the missing data? 2) if I run the model for the full sample (regardless of whether they have attended the focus group or not), Mplus will do some kind of imputation, would be similar to Heckman correction or not? Thank you very much in advance. 


Missing data is properly handled by ML or Bayes assuming MAR, which is the Mplus default setting. WLSMV is less suited to handling missing data (see UG). Heckman modeling can be done in Mplus, but I would simply use ML or Bayes and our default settings. For more on missing data modeling, see Muthén, B., Asparouhov, T., Hunter, A. & Leuchter, A. (2011). Growth modeling with nonignorable dropout: Alternative analyses of the STAR*D antidepressant trial. Psychological Methods, 16, 1733. 


But I also want to see indirect effects and as far as I know ML does not allow estimating indirect analysis. I am not aware of Bayes. Will it allow for estimating indirect results? Best wishes. 


You can use Model Constraint to form your own indirect effects and get their est's and SEs. 


Thank you very much. I think it would have been great and much easier (and maybe better) than applying Heckman correction but unfortunately I do not have the computer capacity to run the ML estimator. It gives an error "*** FATAL ERROR THERE IS NOT ENOUGH MEMORY SPACE TO RUN THE PROGRAM ON THE CURRENT INPUT FILE. THE ANALYSIS REQUIRES 4 DIMENSIONS OF INTEGRATION RESULTING IN A TOTAL OF 0.50625E+05 INTEGRATION POINTS. THIS MAY BE THE CAUSE OF THE MEMORY SHORTAGE. YOU CAN TRY TO FREE UP SOME MEMORY BY CLOSING OTHER APPLICATIONS THAT ARE CURRENTLY RUNNING. NOTE THAT THE MODEL MAY REQUIRE MORE MEMORY THAN ALLOWED BY THE OPERATING SYSTEM.***" And a reviewer suggested that I should use Heckman correction so I would appreciate if you can direct me to somewhere where I can learn more about how to do that. 


You can use ML with integration=montecarlo(5000); 


unfortunately it still gives the same error. 


Please send output to Support@statmodel.com. 


I will send the output as soon as possible but I managed the run my model using estimator = Bayes (it took 2 hours but I have it now! so thank you very much for the suggestion). I have 3 questions: 1) Is it similar to WLSMV estimator, so if the endogenous variable is categorical it is probit coefficients and if it is a latent variable or continuous variable it is a linear regression coefficient? 2) Can I use model constraint to look for indirect effects? 3) when I run my model with WLSMV, I get some fit indices (CFI & TLI) but with Bayes I did not get any of that so how would I know if my model fits? Thank you very much! 


1. Yes. WLSMV and Bayes only differ in Bayes being a fullinformation estimator, therefore handling missing data better. 2. Yes. 3. Bayes in Mplus gives PPP (posterior predictive pvalues)  see our Bayes reports under Papers, Bayesian Analysis. That is, AsparouhovMuthen (2010) papers. 


Dear Dr. Muthen, I am conducting a number of bias corrected bootstrap mediation models involving one predictor variable (each), two mediating variables, and three outcome variables. I used 1000 bootstrap replications and the CINTERVAL(BCBOOTSTRAP) option to run my models. I have run several of these models, but for one of my models I obtain 2.5% and 97.5% confidence interval estimates for the indirect effects that are beyond 1 and 1. I recognize that my models do not imply mediation, however, I am concerned that I might have missed something... These outofrange values do not occur for any of my other models. Could you please point me to a few references that might help me understand why this might have occured? Thank you in advance. 


The size of an indirect effect depends on the scales of the variables and is not restricted to be less than 1. 


Thank you for your quick response. 


Hello, I'm running a mediation model with bias corrected bootstrap. I'm confused though, as the output from the model indirect command gives me a pvalue of .10 for the indirect effect, but the cinterval command says that my indirect effect ranges from .02 (lower 2.5%) to .052 (upper 2.5%). Give that these are bounded within a 95% CI, shouldn't the pvalue for indirect effect be <.05? Thanks for your help. 


And, to follow up, which of the two should I report when reporting te significance of the biascorrected bootstapped indirect effect? (I used cinterval(bcbootstrap) ). Thanks again 


The zvalue should be compared to a symmetric bootstrap. The biascorrected bootstrap is not symmetric. It may be more appropriate for an indirect effect. 


Thank you for the suggestion. I reran the model with CINTERVAL(BOOTSTRAP) rather than BCBOOSTRAP. The 95% CI for the indirect effect is still .001 to .05, implying a significant indirect effect, but the pvalue of the indirect output is .09. Which would you suggest interpreting in terms of concluding whether or not the indirect effect is significant? Also, do you know why the two would be different? Thanks 


We recommend BCBOOTSTRAP in line with the mediation book by MacKinnon. We recommend reporting the 95% CI. 


Hello, I'm running a latent growth curve mediation model where the growth factors are my mediators. When I use BCBOOTSTRAP for bootstrapping, the results suggest the indirect effects for both the intercept and slope term are significant. However, the "A path" from slope to my IV is not significant according to the CIs (.10, .02). When I use the BOOTSTRAP option, only the indirect effect for the intercept is significant, and both the a and b paths are also significant, as one would expect. I'm wondering how to make sense of this discrepancy, and which bootstrap option to use? I know you usually recommend BCBOOTSTRAP, but that seems to be providing some odd results in this case. Thanks! 


We now recommend BOOTSTRAP per recent research that we discuss in our book: http://www.statmodel.com/Mplus_Book.shtml You may also want to try Estimator = Bayes to get another assessment. 

sarah M posted on Monday, April 08, 2019  11:59 am



Dear Dr. Muthen, I wanted to set a seed number when obtaining a bootstrap confidence interval. Is there a way to specify seed number in order to replicate the results? Thanks. 


We currently do not have such a command. You can try to double the number of bootstrap draws and make sure that the confidence intervals do not change substantially. 


I note in a post above that, as of 2005, there wasn't an option to set the seed number for Type = Bootstrap. Is this possible now? Thankyou, 


Still not available. Choosing a large enough bootstrap replications should eliminate the need to study the variability of the estimates. 


Hello, Is there a way to have Mplus generate pvalues that directly correspond to the biascorrected confidence intervals obtained via bootstrapping (i.e., BCBOOTSTRAP)? For a recent manuscript, we ran several serial mediation analyses based off of a priori hypotheses. We have received reviewer requests that we make a familywise error adjustment. For this, we would need pvalues directly equivalent to the biascorrected CIs. Is this possible to obtain? Thank you! Sarah 


It is possible but not very easily available. Here is what you would need to do. Make sure you use a large amount of bootstrap draws, at least 1000. Add plot:type is plot3; Run the analysis and click on the plot icon. Select "Bootstrap distribution". Select the parameter you want and use 1000 bins for this exercise as you will need the extra precision. This is the raw (uncorrected) bootstrap distribution. You need two things from this bootstrap distribution. The percentile of draws p1 below zero and the percentile of draws p2 below the point estimate. To get these, right button click on the plot and select save plot data. The save data file has two columns. The first column is the bin value and the second column is the count (the actual bootstrap values are not currently available). In excel or google spreadsheet add the count values up to the bin value closes to 0 and closest to the point estimate (from the Mplus output). If Phi is the standard normal distribution function the bias corrected onesided Pvalue will be computed by Phi(2*Phi^1(p2)+Phi^1(p1)) Here 2*Phi^1(p2) represents the bias correction and p1 is the standard bootstrap one sided pvalue. This will work for positive point estimate. For negative point estimate you would compute p1 as the proportions of bootstrap draws above zero. If p2=0.5, the bias correction is zero and the bias corrected Pvalue is the same as the bootstrap Pvalue. 


The one sided Pvalue formula given in the previous message has an error. There is a missing negative sign. It should be Phi(2*Phi^1(p2)+Phi^1(p1)) This is now described in more details in this FAQ http://statmodel.com/download/FAQBootstrap%20%20Pvalue.pdf 

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